Head off to travel after home is run down (9)
I believe the answer is:
denigrate
'is run down' is the definition.
(I've seen this before)
'head off to travel after home' is the wordplay.
I cannot quite understand how this works, but
'home' could be 'at' (synonyms) and 'at' is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for denigrate that I've seen before include "Blacken" , "Unfairly criticise" , "Defame" , "Slight" , "put down" .)